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io„gl Bureau of Standards 





NBS 



TECHNICAL NOTE 



361 



Saturated Liquid Densities of 
Oxygen, Nitrogen, Argon, and 
Parahydrogen 



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U.S. DEPARTMENT OF COMMERCE 
National Bureau of Standards 



NATIONAL BUREAU OF STANDARDS 

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UNITED STATES DEPARTMENT OF COMMERCE 

C. R. Smith, Secretary 
NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director 



NBS 



TECHNICAL NOTE 361 



ISSUED JANUARY 31, 1968 



SATURATED LIQUID DENSITIES OF 
OXYGEN, NITROGEN, ARGON, AND PARAHYDROGEN 



H. M. RODER, R. D. McCARTY AND V. J. JOHNSON 

Cryogenics Division 

Institute for Basic Standards 

National Bureau of Standards 

Boulder, Colorado 80302 



NBS Technical Notes are designed to supplement the 
Bureau's regular publications progranfi. They provide a 
means for making available scientific data that are of 
transient or limited interest. Technical Notes may be 
listed or referred to in the open literature. 



For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402 

Price 50 cents. 



COmENTS 

List of Tables iv 

List of Figures Iv 

Abstract , 1 

1. Introduction 1 

2 . Description of tables and graphs 2 

3. Discussion 5 

k. Limitations and Usage 9 

5. Oxygen 13 

6. Nitrogen 29 

7. Argon kl 

8. Parahydrogen 55 

9 . References 65 

10. Appendix: Units and Conversions 66 

Actnovledgement 66 



111 



List of Tables 

Table 

1 Oxygen near room temperature I3 

2 Uncertainties In the data for oxygen ik. 

3 Saturated liquid oxygen I5 

k Nitrogen near room temperature 29 

5 Uncertainties In the data for nitrogen 30 

6 Saturated liquid nitrogen 31 

7 Argon near room temperature kl 

8 Uncertainties In the data for argon 42 

9 Sat\irated liquid argon k3 

10 Parahydrogen near room temperature 55 

11 Uncertainties in the data for parahydrogen 56 

12 Saturated liquid parahydrogen 57 

Figure List of Figures 

1 Generalized phase diagram; pressure vs. voliime 3' 

2 Generalized phase diagram; volume vs. pressure 9 

3 Specific volume vs. pressure for oxygen 27 

k Volume correction factor for oxygen 28 

5 Specific volume vs. pressure for nitrogen 39 

6 Volume correction fa c tor for nitrogen kO 

7 Specific volume vs. pressure for argon . ♦ 53 

8 Voltime correction factor for argon , .... 5^ 

9 Specific volume vs. pressiore for parahydrogen 63 

10 Volume correction factor for parahydrogen . • 64 

Extra scales for figures 67 



iv 



SATURATED LIQXHD DENSITIES OF 
OXYGEN, NITROGEN, ARGON, AND PARAHYDROGEN 

H. M. Roder, R. D. McCarty, and V. J. Johnson 

Integrated tables of pressure, vol-ume, and temperature 
for the saturated liquid, from the triple point to the critical 
point, of oxygen, nitrogen, argon, and parahydrogen are pre- 
sented. The tables include entries of integral values of 
temperature in both Kelvin and Rankine , and integral values 
of pressure in both atmospheres and psia. Volumes and densi- 
ties in three different units and a density ratio are tabulated 
for each entry. Estimates of the uncertainty of the tabulated 
data are given. 

Key ¥ords: Pressure, volume, density, temperature, saturated 
liquid, oxygen, nitrogen, argon, parahydrogen, 
uncertainties . 

1. Introduction 

In this report, standard density data for the saturated liquid of 
four commercially important gases are presented. The report was pre- 
pared at the specific request of users such as the Compressed Gas 
Association, the Department of the Air Force, and the State of Calif- 
ornia, "who must either pay for goods delivered^ or supervise delivery 
to customers. These agencies have experienced a certain amount of non- 
uniformity in costs and billings that arise because different suppliers 
use slightly different methods or values for the physical properties of 
these gases . 

The report is a logical extension of an earlier effort, pamphlet 
P-6, "standard Density Data Atmospheric Gases and Bydrogen," by the 
Compressed Gas Association. In this pamphlet, values of pressure, temp- 
erature, and density for the Normal Boiling Point (NBP) and Standard 
Temperature and Pressure (STP) were presented. 

Now we need more than just the two state points NBP and STPj we 
need a definition of the saturated liquid curve as well. Also, the 
sources selected for this document are considered to be the best avail- 
able today. The compilations of oxygen, argon, and parahydrogen, each 



representing at least tvo man years of effort, were not available in 
1965. The source for nitrogen remains unchanged. Ntperical values 
differ from the earlier selections by as much as 0.1^. The advantages 
in using the present sources are: 

1. Each of the compilations selected present a consistent set of values 
from a single source for each fluid. 

2. All available data, in particular the correlation of the sl,ngle 
phase PVT data vith the saturation hoiindaries and the vapor pres- 
siire cwrve, have been considered, not ju§i the value of the WBP, 

3' The equations of stat^ in the form of computer programs, allow deter- 
mination of values, bo^th at liquid temperatures and at room tempera- - 
tures . 

k. The equations of state used present a consistent set of values for 
the satioration boundary as well as for the compressed fluid states. 
As flowmeter technology improves, an extension to the compressed 
fluid state will become imperative. Such a change can be accom- 
plished without a further adjustment in niamerical values. 

We hope that the values presented here will sei^e as "agreed-on" values 

for some time to come. 

Because NBS has been called upon to make a selection of values, 

a considerable portion of the text is devoted to discussion and an 

estimate of errors. This should satisfy the scholar and scientist. 

Because the use to which the document will be put is eminently practical, 

the tables and graphs are presented primarily in practical units. This, 

and the section on pitfalls or limitations of these tables, should thus 

be usefiol to the engineer. 

2. Description of Tables and Graphs 

To understand the properties that are presented in the tables and 
graphs, it is helpful to recall one of the "standard" phase diagrams. 
Try to recollect the presentation of isotherms in P-Y coordinates as 
given in figure 1. You may recall the rectangular hyperbolas of 




Gas Isotherm 
Critical isotherm 
Liquid isotherm 



"FLUID" REGiON 




VOLUME 

Figure L. Gteneralized phase diagram; Pressure vs. Volume 

3 



PV = const of the ideal gas, and the critical isotherm first presented 
in a discussion of the Van der Waals equation of state. This report 
concerns only the equlllhrlum boundary between the single phase (com- 
pressed) liquid region and the two phase liquid/gas region. The bound- 
ary is emphasized in figure 1 and extends from the triple point to the 
critical polnt"*^. 

The first table for each fluid presents values of pressure, temper- 
ature, and density near room temperature. One atmosphere is usually 
accepted as "standard" pressure; however, the values of temperature 
chosen as "standard" or "normal" vai*y. ¥e, therefore, present values 
at C, which point is usually called "Standard Temperature and Pressure" 
(STP), and at 68 F as well as 70 F, both of which are referred to as 
"Normal Temperature and Pressiire" (NTP) . 

The second table for each fluid presents values for the \incertaln- 
ties in the data. For the values of the saturated liquid, the uncertain- 
ties include both the errors in the experimental values and the contri- 
bution to the error by using an analytical function to represent the 
experimental values. Errors for values near room temperature are seen 
to be much smaller because PVT measurements near room temperature can 
be made to great accuracy and a better fit to the equation of state 
can be made. 

The third and principal table presents values of increasing 
pressures (vapor pressure) and corresponding temperatures. These two 
variables define the vapor pressure curve. The table is a merged 
table of even values of pressure in both atmospheres and psia and of 
temperature in both K and R. The corresponding entries of density, 
volume, and density ratio follow. There are two columns of density 
ratios. The first column is labelled "Liquid Voltmie Correction Factor" 
and will be used as such. Physically it is the ratio of the density 
in question, referred to the density at the Normal Boiling Point (NBP) , 



Mr 

Strictly speaking, in this phase diagram the NBP and the triple point 
are lines extending from liquid to vapor side at the pressure indicated. 



which in turn corresponds to a pressure of 1 atmosphere. For examples 
of use see case 1, the alternate computation of case 3^ case k, and 
case 5 on page 11. The second column is labelled "NTP (70 F) Volume 
Correction Factor". Physically this ratio is also a ratio of densities^ 
namely the ratio of the density in question referred to the density at 
NTP. F or this column, HTP is selected to be 7Q F and 1 atmosphere . The 
units of the two densities are chosen such that the NTP Volume Correction 
Factor yields directly the equivalent number of cubic feet of gas at 
NTP (70 F) per measinred gallon of liquid. For an example of use, see 
case 3 on. page 11. Entries in pressure are closely spaced so that 
interpolation between values should not be required. For parahydrogen, 
the increment in pressiire is 1 psia from 1 to I50 psia, and for the 
other fluids the increments are 2 psia between 2 and 200 psia and 5 psia 
between 205 and ^00 psia. The tables include entries for the Triple 
Point, the Normal Boiling Point, and the Critical Point, and these 
points are set off by double spacing in the table. Conversion of units 
are given in the appendix. Please note that the number of significant 
figures presented in the tables is not justified on the basis of accuracy, 
but are given to maintain internal consistency. 

The first graph for each fluid is a plot of specific volume vs. 
pressure. The graph can be understood quite easily if you imagine 
figure 1 rotated about the k^° axis, i.e., the coordinates interchanged. 
The very practical reason behind this presentation is that the variable 
most easily and often measured on tanks, etc. is the pressure; thus it 
is sensible to have the pressure displayed as the independent variable. 
Because storage and transport tanks are not usually subjected to 
pressures in excess of I50 psi, this is the limit chosen for the graphs. 

The second graph is somewhat more specialized. It gives the 
Liquid Volume Correction Factor (or density ratio) for a pressure range 
of about 50 psia from slightly below atmospheric pressure"'. Transfers 
of liquid usually take place at pressure conditions different from 
the Normal Boiling Point (NBP), yet the quantity of liquid transferred 
is desired in figures equivalent to the amount at the NBP. The graph 



assumes that either a pressure or a temperature indicator may be used 
to detenaine the condition of transfer; thus it is actually a pressiore- 
temperature plot of the saturated liquid. It is a rotation about the 
k-^° axis of the more familiar vapor pressure vs. temperature plot vith 
the coordinates interchanged. The temperature scale and the Liquid 
Volume Correction Factor scale are arranged in nomograph style for 
convenience of use. Also^ an auxiliary scale for psig has been added 
at the bottom of the graph , and an extra auxiliary scale at the end 
of the report. If the local barometer is different from standard sea 
level, either pslg scale can be cut out and positioned for the appro- 
priate altitude. 

3. Discussion 

The nature of progress in cryogenics is such that today's "best" 
value may be superseded tomorrow. In the initial effort. Pamphlet P-6 
of the Compressed Gas Association (1965), only values for the NBP and 
values at NTP were presented. The present report includes values for 
the saturated liquid boundary. In logical sequence, the next refinement 
has to include the PVT values in the compressed fluid states because ve 
know that in many applications the fluid entering pump intakes is sub- 
cooled to prevent subsequent cavitation. 

We have selected the following sources: Stewart (I966) for oxygenj 
Strobridge (1962) for nitrogen; Gosman, et al. (I968) for argon; and 
Roder, et al. (I965) as well as Hilsenrath, et al. (1955) for para- 
hydrogen. These sources differ from the earlier selection for the 
CGA effort. As you can see, the compilations for oxygen, argon, and 
parahydrogen were not available in 1965* There is, however, a more 
compelling reason in selecting a compilation as a source. We now require 
not just a vapor pressure curve but a correlation of that curve with 
all available PVT data of the single phase (compressed liquid). A 
further reason is that these sources will permit extension into the 
compressed liquid states when and if such an extension becomes desirable. 



One last advantage accrues when we select these compilations as sources. 
Except for hydrogen, we can get the values at or near room temperatirre , 
i.e., the STP and NTP values directly from the equation of state, inter- 
polated to the accuracy of the original data. 

The last point requires a bit more discussion because it ties in 
with the uncertainties in the values presented at or near room tempera- 
ture. In the present report we have used a high order interpolation - 
the equation of state - to get STP and NTP values. We are justified in 
using a high order interpolation because the various experimenters went 
to considerable lengths to get the most accurate PVT values at condi- 
tions close to room temperature. According to Cragoe (19^1 ), relative 
measurements of pressure and volume near room temperature can be made 
to a few parts per million, and the scatter between PVT values of 
different observers can to a large extent be explained by the use of 
different fvmdamental constants. In tables 2, 5^ 8, and 11, we indicate 
an uncertainty of 0.01'^ as the -uncertainty in molar volume at STP) this 
is the familiar 22.4 liters per mole that is encountered in elementary 
texts. The uncertainty is based on a consideration of the ice point 
temperature, T , rather than on a comparison of different experiments. 
The fundamental constant T is now defined to be 273-15 K, but the 
average over a large number of determinations of different investigators 
for different gases was 273.I65 (Beattie, 19^1). We have taken the 
difference between these two niimbers as an indication of the true 
uncertainty in the molar volumes . Even if the values of different 
authors are compared directly, the differences are not much larger than 
O.Olfo. Take for example hydrogen, the molar volume is 22^1-28.5 cm^/mole 
according to Woolley, et al. (19U8), while it is 22433.6 cm /mole 
according to Michels, et al. (1959). The difference Is 0.022/o. In 
contrast to this there is no difference between recent measurements on 
oxygen by Weber (1968O and those of Michels, et al, (l954) if one uses 
identical values for the fundamental constants R and Tq. 



The earlier effort (CGA, I965) "was slightly inconsistent in that 
for argon and oxygen linear interpolation-*^ was used, while the higher 
order interpolations were used for hydrogen and nitrogen. The room 
temperature values presented in this report for NTP of oxygen and 
argon will differ by about 0.02^ from those given CGA in I965 , while 
those for nitrogen and parahydrogen are unchanged. On the other hand, 
the densities of the saturated liquid at the NBP have changed by 
0.1^ for oxygen and nitrogen, and are virtually -unchanged for argon 
and parahydrogen. 

Another word on errors given in tables 2 , 5 ^ 8 ^ and 11; in 
obtaining entries for our primary tables, we have assumed either 
temperature and density or temperatiore and pressure to be exact. 
Thus only uncertainties in pressure in the first case and density 
in the second case are of concern and should be presented. However, 
uncertainties for all three variables (P-V-T) are presented. This 
allows the user to enter the tables with any combination of variables 
and obtain the uncertainty in the resulting value. Other considera- 
tions are also important. One is that our practical temperature scales 
differ from the thermodynamic one — the absolute one. This is the 
indication in the tables of error as far as temperature is concerned. 
Occasionally the unceDrtainties given for temperature may simply Indicate 
the extent to which we are able to measure or achieve a certain tempera- 
ture. The situation with pressure is similar. In our laboratories, with 
high precision apparatus, we can achieve a resolution of, say, 0.001 atm. 
However, an equation of state is normally a function of temperature and 
density, that is, P = f(T,p), leading most compilers to present un- 
certainties in terms of pressure deviations assuming the density to be 
exact i In this compilation, where deviations in pressure were avail- 
able, we Included them as additional information. 



Exactly as recommended by Hllsenrath, et al. (1955 )> hut not taking 
advantage of the accuracy inherent in the data. 



UJ 

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> 




PRESSURE 

Figure 2. Generalized Phase Diagram; Volume vs. Pressure 



k. Limitations and Usage 



In practice, a number of problems are encountered that would intro- 
duce errors beyond what we might expect from the uncertainties inherent 
in the data. A few of the practical problems are indicated below. 

a) The informed engineer recognizes that the processes of transfer, 
transport, pressurizing, siphoning, and stratification in storage tanks are 
all non-equilibriiim events . The properties presented in this report are 
equilibrium properties. 

b) We have indicated that pump intakes, or, for that matter, flow 
meter intakes, are usually subcooled to prevent cavitation. As the need 
arises, the user can extend the graphs of specific volume vs. pressure, 
figures 3, 5^ 1} and 9^ "by adding appropriate isotherms for the compres- 
sed liquid states . This can be done by referring to the sotirce docu- 
ments and by noting that the liquid isotherms in the range of the graphs 
are almost straight lines . This is indicated schematically in figure 2 



■where the Isotherms for oxygen, nitrogen, and argon are shown as 
straight lines. For parahydrogen the isotherms may show some slight 
curvature, as indicated. 

c) The purity of the product will also play a role. The proper- 
ties presented here are for the piire product made available under 
laboratory conditions, and may not be appropriate for certain purity 
grades of commercially available gases without some adjustment for the 
known impurities . 

d) The values presented in this report were obtained from 
various computer programs . We have in the past made these programs 
available to any user requesting them. However, different computers 
will retiirn different results from the same programs; in particiilar, 
they will round differently. The user should be aware of the follow- 
ing: The accuracy of the data for liquid conditions is on the order 
of 0.1 to 0.3fo, while the accuracy of the room temperature values is 
on the order of 0.01 to 0.02^. We have, therefore, printed no more 
than 5 digits anywhere. Please bear in mind that even the fourth digit 
is uncertain for most values , that is , the digits printed are only to 
maintain internal consistency of the tables and to allow you to check 
out your computer programs. If occasionally pairs of values or reci- 
procals do not seem to correspond, then the fault can be traced to 
roxmding errors. 

Examples of usage are included because they may be of value to 
individuals not skilled in the use of graphs . We have mentioned the 
compensation for altitude. As an example, atmospheric pressure in 
Boulder, Colorado, is near 12 psia. If we had a pressure gage which 
measured pressure with respect to atmospheric pressure, i.e., a gage 
which reads psig and not psia, then we could cut out the extra auxi- 
liary scales at the end of the report and paste them on graphs k, 6, 
8, and 10 over the main scale with the zero of the auxiliary scale 
lined up with the 12 on the primary scale. 

When we use the tables and graphs to prepare billings, a number 
of combinations are possible. The ones likely to occur are discussed 
below. 

10 



Case 1. Price given in terms of gallons at NBP, 

flowmeter reading '25 gallons^ tank pressure reading 26 psia, 

fluid liquid nitrogen, price $ 0.40 per gallon at NBP. 

¥e would go to figure 6 and enter with 26 psia on the primary 

scale to read out a value of 0.970 for the liquid volume correction 

factor (or the use of table 6 gives a value of 0.9697)' 

The billing computation is: 

gallons X liquid vol\ame correction factor x price 

25 gal X 0.970 X $ 0.40 /gal = $ 9.7O. 

Case 2. Price given in terms of weight, 

flowmeter reading 25 gallons, tank pressure reading 26 psia, 

fluid liquid nitrogen, price $ O.O6 per poimd. 

¥e would go to table 6 enter with 26 psia and find in the col-umns 

of density 6-53^ lb /gal. 

The billing computation is: 

gallons X actual density X price 

25 gal X 6.5341 lb /gal X $ 0.06/lb = $ 9.80. 

Case 3. Price given in terms of cubic feet at NTP (70 F) , 
flowmeter reading 25 gallons, tank pressure 26 psia, 
fluid liquid nitrogen, price $ 4.32 per 1000 ft^ (NTP) . 
We would go to table 6 and enter with 26 psia to read a value of 
90.19 ft^/gal for the NTP (70 F) vol-ume correction factor. 
The billing computation is: 

gallons X NTP (70 F) volume correction factor X price 
25 gal X 90.19 ft^/gal X $ 4.32/1000 ft^ = $ 9.74. 
Alternate Computation ; Since the column labelled "NTP (70 F) Volume 
Correction Factor" is the combination of the liquid voliime correction 
factor multiplied by the equivalent volume at NTP (70 F), we could have 
used figure 6 with a pressure of 26 psia to read a value of 0.970 for 
the liquid volume correction factor and table 4 to obtain the equi- 
valent vol\ame of 93-006 ft^/gal for a temperature of 70 F. 
The billing calculation then becomes: 

gallons X liquid volume correction factor x equivalent volume X price 
25 gal X 0.970 X 93-006 ft^/gal x $ 4.32/1000 ft^ = $ 9-7^. 



11 



Case h. Price given in tenns of Standard Cubic Feet (SCF) at STP(OC), 
and our flo-wmeter is geared to read in cubic feet. 
Flowmeter reading 2158 f t° , tank pressure reading 26 psia, 
fluid liquid nitrogen, price $ k.66 per 1000 SCF. 
We will assume that the gearing ratio of the flowmeter is based 
on the volume change NBP to STP. If so, then the liquid volume correc- 
tion factor still applies and we have to go to figure 6 (or 
table 6) as before to get a value of 0.970. 
The billing computation is: 

cubic feet X liquid volume correction factor x price 
2158 ft^ X 0.970 X $ U. 66/1000 SCF = $ 9.75. 

Case 5* Any of the above, except that we have a temperature sensor on 
our storage or transport tank instead of the pressvire gage. 
The temperature reading is l48 R. We would go to figure 6 and 
use a straight edge to read across from the temperature scale 
at l48 R to the liquid voliame correction factor scale to get a value 
of 0.972. The value obtained from table 6 for the liquid volume 
correction factor is 0.9717' The corresponding value for density 
is 6.5477 lb /gal. 



12 



5 • Oxygen 

The data for oxygen tabiilated here are from Stewart (I966) and 
Weber (1968) . The data for temperatures of 65 K and above were calcu- 
lated by sim-ultaneous solution of the vapor pressure equation and the 
equation of state reported by Stewart. These calculations were performed 
by first solving the vapor pressure equation for either pressure or 
temperature, and using the resulting P and T as input to the equation of 
state to obtain a corresponding density. 



Table 1 



Density of oxygen at 1 atmosphere near room temperature 



Temperature 


Density 


gram-mole /cm^ 


lb/ft° 


lb /gal 


C 
68 F 
70 F 


0.000044660 
0.000041602 
0.000041445 


0.089214 
0.083106 
0.082791 


0.011926 
0.011110 
0.011068 


Temperature 


Volume 


cm° /gram-mole 


f t^ /lb 


gal/lb 


C 

68 F 
70 F 


22391 
24037 
24129 


11.209 
12.033 

12.079 


83.849 
90.012 

90.355 


Temperature 


Density Ratios and Equivalent volumes 
density at NBP 


density at the temperature indicated 


C 
68 F 
70 F 


dlmens ionles s 


Ib/ft^ 


798.18 
856.85 
860.11 


106.70 
114.54 
114.98 



13 



Values near room temperature are given in table 1. They differ 
from those given in the CGA pamphlet "by O.O2/0 primarily "because a higher 
order interpolation is used here. Uncertainties in the data are given 
in table 2. The main list of values is contained in table 3' The pres- 
sure and temperature of the first two entries in table 3 are from the 
vapor pressure equation as described above, but the densities are from the 
experimental data by Weber. The value of the KBP density in table 3 is 
different by 0.2fo from that listed in the CGA pamphlet. The present value 
is considered to be better because it includes additional PVT data. 



Table 2 
Uncertainties in the data for oxygen 



variable 


uncertainty 


range of temperature 


temperature 


0.05 K 


below 90 K 




0.02/0 


between 90 and 15i<- K 




0.1/0 


near critical 




0.015 K 


room temperature 


volume 


0.1/0 


between 5^-353 and 60 K 




0.5/0 


between 65 and I50 K 




larger 






than 0.5/0 


between I50 K and critical 




0.01/0 


room temperature 


pressure 


0.1/0 


below 90 K 




0.02^ 


between 90 and 154 K 




0.1/0 


near critical 




0.01/0 


room temperature 



14 



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6. Nitrogen 

The data tabulated for nitrogen are "based on the paper by 
Strobridge (I962) . The saturated liquid values vere calculated by sol- 
ving simultaneously the vapor pressure equation and the equation of 
state. First the vapor pressure equation was solved for either pressure 
or temperature depending on the integral value desired, then using the 
resiilting P and T, the equation of state was solved for the correspond- 
ing density. All of the tabulated values were obtained in this manner 
except the critical point. At the critical point the vapor pressiire 
equation was used to calculate the pressure from an input temperature 
of 126.26 K but the density was calculated using the theory of 

Table 4 

Density of nitrogen at 1 atmosphere near room temperatiore 



Temperature 


Density 


gram-mole/cm° 


Ib/ft^ 


Ih/gal 


C 
68 F 

70 F 


0.000044635 
0.000041582 
0.000041424 


0.078066 
0.072725 
0.072450 


0.010436 
0.009722 
0.009685 


Temperature 


Volume 


cm^ /gram-mole 


ft^/lb 


gal/lb 


C 

68 F 
70 F 


22404 
24049 
24141 


12.810 
13.750 
13.803 


95.823 
102.860 
103.251 


Temperature 


Density Ratios and Equivalent volumes 
density at NBP 


density at the tempera tiore indicated 


C 

68 F 
70. F 


dimensionless 


^ - ftVgal 
Ib/ft^ 


645.67 
693-08 

695-71 


86.31 
92.65 
93.006 



29 



Figure 4 

VOLUME CORRECTION FACTOR 

for 

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rectilinear diameters and the saturation densities tabulated by 
Strobridge . 

Values near room temperatiire are given in table 4; as the 
source has not changed, the values remain the same. Uncertainties in 
the data are given in table 5 • Wear the critical point , the deviations 
between calculated and experimental data goes from 0.2^ at 125 K to 
5^ at 126 K. The critical density given in table 6 is uncertain by 
5^ as well. The buLb of the values are found in table 6. The value of 
the density at the NBP in table 6 should be the same as in the CGA 
pamphlet, yet they differ by 0.2^. This is surprising as the source 
has not changed, and we can only suspect an error in the printing of 
the pamphlet. 

Table 5 
Uncertainties in the data for nitrogen 



variable 


uncertainty 


range of temperature 


temperature 


0.% 
0.1/0 
0.015 K 


Gk to 72 K 
72 to 125 K 
room temperatiire 


vol-umie 


increases to 5^ 
O.Olfo 


up to 125 K 

at 126 K 

room temperature 


pressure 


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0.01^ 


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72 to 126 K 
room temperature 



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7 . Argon 

The data for argon given here are from Gosman, et al. (1968) . 
The entire P7T tabulations were calculated by a simultaneous solution 
of the vapor pressure equation and the equation of state reported by 
these authors. The calculation of each point vas performed by solving 
the vapor pressure equation for either P or T depending on "which "was 
the integral value input. Using the P and T so obtained a corresponding 
density vas found from the equation of state. 



Table 7 



Density of argon at 1 atmosphere near room temperature 



Temperature 


Density 


gram-mole /cm*^ 


Ib/ft^ 


lb/gal 


C 
68 F 
70 F 


0.000044659 
0.000041601 
0.000041444 


0.111373 
0.103749 
0.103356 


0.014888 
0.013869 
0.013817 


Temperature 


Volume 


cm^ /gram-mole 


ft^/lb 


gal/lb 


C 
68 F 
70 F 


22392 
24038 
24129 


8.979 
9.639 
9.675 


67.166 
72.102 
72.376 


Temperature 


Density Ratios and Equivalent vQlimes 
density at NBP 


density at the tempera t\rre indicated 


C 
68 F 
70. F 


dimensionless 


i^ = ftVgal 
lb/ft"" 


781.34 
838.75 
841.94 


104.45 
112.13 
112.55 



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Values near room temperature are given in table "J. These values 
differ from those in the CGA pamphlet by about O.O2/0 primarily because 
a higher order interpolation is used here. Uncertainties in the data 
are shown in table 8. The tabulation for the saturated liquid line is 
foiind in table 9. The value of the density at the NBP differs from 
that in the CGA pamphlet by 0.04fo. The new correlation includes quite 
recent data both on PVT and on the temperature scale corrections and 
should, therefore, be more accurate. 

Table 8 
Uncertainties in the data for argon 



variable 


Tincertainty 


range of temperature 


temperature 


0.0^0 
0.02fo 
0.015 K 


84 to 87 K 
82 to 154 K 
room temperature 


volume 


O.lfo 

increase to l/o 
O.Olfo 


triple point to 1^5 K 

linearly from l45 K to critical 

room temperature 


pressure 


O.lfo 

0.0^0 
O.Olfo 


84 to 87 K 
87 to 154 K 
room temperatizre 



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8 . Parahydrogen 

"While the document or so\irce for parahydrogen has changed, the 
numerical values remain the same. The tables for the saturated liquid 
■were calciolated using the explicit equations for vapor pressiire (Weber, 
et al. 1962) and saturated liquid density (Roder, et al. I963) which 
were incorporated unchanged into the final compilation (Roder, et al. 
1965) . The values for temperatures near room temperature vere taken 
from Hilsenrath, et al. (1955)^ using a high order interpolation. This 
is the source used by the experimenters in their determination of the 
liquid densities. The CGA pamphlet cites Dean (1961), who also presents 
a high order interpolation of Hilsenrath's values. 

Table 10 
Density of parahydrogen at 1 atmosphere near room temperature 



Temperature 


Density 


gram-mole/cm^ 


Ib/ft^ 


lb/gal 


C 
68 F 
70 F 


0.000044588 

.000041547 

0.000041390 


0.005611 
0.005229 
0.005209 


0.000750 
0.000699 
0.000696 


Temperature 


Volume 


cm° /gram-mole 


ft°/lb 


gal/lb 


c 
68 F 
70 F 


22428 
24069 
24160 


178.21 
191.25 
191.97 


1333-1 
1430.6 
1436.1 


Temperature 


Density Ratios and Equivalent volumes 
density at NBP 


density at the temperature indicated 


c 
68 F 
70 F 


dimensionless 


Ib/ft^ 


787.50 
845.13 
848.34 


105.273 

112.98 

113-41 



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Values near room temperattire are given in table 10 . As stated be- 
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P-6. Uncertainties in the data are shown in table 11. The main table of 
values pertaining to the satiirated liquid are foumd in table 12. An 
astute observer may detect a difference of one part in 4000 in the 
density at the NBP between this table and pamphlet P-6, but that differ- 
ence is caused only by accumulative rounding errors. 

The properties presented here pertain to parahydrogen . Specifi- 
cations for delivery of parahydrogen are usually stated as 95^ para- 
hydrogen with the remainder being orthohydrogen . As a matter of fact, 
producers do not send less than 97^ parahydrogen to storage tanks, and 
the liquid when shipped is, or is very close to being, equilibrium 
hydrogen. Equilibrium parahydrogen is 99 '79^ para at the NBP, and the 
difference between it and 95'^ parahydrogen amounts to about 0.008 K or 
about 2 ram in pressure. It is easy to see that sophisticated equipment 
is required to detect ortho-para composition. The matter of composition 
is mentioned because the amount of orthohydrogen present has a very 
pronounced effect on the length of storage. 

Table 11 
Uncertainties in the data for parahydrogen 



variable 


uncertainty 


range of temperature 


temperature 


0.02 K 
0.015 K 


triple point to critical point 
room temperature 


vol-ume 


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near critical 
room temperature 


pressure 


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room temperature 



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9 ♦ References 

Seattle, James A. (l94l) , "The Thermodynamic Temperature of the Ice 
Point," Temperature, Its Measurement and Control in Science and 
Industry , pp. 78-88 (Re inhold Publ. Corp., Nev York, N. Y.). 

Cragoe, C S. (19-^1), "Slopes of the PV Isotherms of Some Thermometric 
Gases at Pressures Below Two Atmospheres," Temperature, Its Measurement 
and Control in Science and Industry , pp. 89-I26 (Reinhold Puhl. Corp. , 
New York, N. Y.). 

Dean, J. ¥. (1961), "A Tabulation of the Thermodynamic Properties of 
Normal Bydrogen from Low Temperatures to 300°K and from 1 to 100 
Atmospheres," Natl. Bur. Stds. Tech. Note No. 120. 

Gosman, A. L. , R. D. McCarty, and J. G. Hust (1968) , "Thermodynamic 
Properties of Argon from the Triple Point to 3OO K at Pressures to 
1000 Atmospheres," NBS Monograph (in press). 

Eilsenrath, Joseph, et al. (Nov. 1, 1955)^ Tables of Thermal Properties 
of Gases, Comprising Tables of Thermodynamic and Transport Properties 
of Air, Argon, Carbon Dioxide, Carbon Monoxide, Bydrogen, Nitrogen, 
Oxygen, and Steam, NBS Circular ^6k (U. S. Government Printing Office, 
Washington, D. C). 

lUPAC Revised Atomic Weight Values, Chem. Engr. News 37, ii-2-43 
(Nov. 20, 1961). 

Mechtly, E. A. (1964), The International System of Units, Physical 
Constants and Conversion Factors, NASA P-7012, Scientific and Technical 
Infonnation Division (National Aeronautics and Space Administration, 
Washington, D. C). 

Michels, A., W. DeGraaff, T. Wassenaar, J. M. H. Levelt and P. Louwerse 
(1959) } "Compressibility Isotherms of Hydrogen and Deuterium at 
Temperatures between -175 *'C and +150°C (at Densities up to 9^0 Amagat)," 
Physica 25_, 25-41. 

Michels, A., H. W. Schamp, and W. DeGraaff (1954), "Compressibility 
Isotherms of Oxygen at 0"*, 25 °C and 50°C and at Pressures up to 
135 Atmospheres," Physica 20, 1209-14. 

Roder, H. M. , D. E. Diller, L. A. Weber, and R. D. Goodwin (19^3), "The 
Orthobaric Densities of Parahydrogen, Derived Heats of Vaporization, 
and Critical Constants," Cryogenics 3.> 16-22. 

Roder, H. M. , L. A. Weber, and R. D. Goodwin (I965), Thennodynamic 

and Related Properties of Parahydrogen From the Triple Point to 

100 °K at Pressures to 340 Atmospheres, NBS Monograph 94 (U. S. Government 

Printing Office, Washington, D. C). 



65 



Figure 10 
VOLUME CORRECTION FACTOR 
for 
PARAHYDROGEN 




20 



I I I I I I I 



-4 



10 



30 40 50 

I I I I I I I I I I I I I 



20 



60 70 80 90 

PRESSURE, psia 

I I I I I I I I I I I I I I I 



100 



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30 40 50 60 70 

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120 



J \ I L 



130 



140 

I I I I I I 



80 



90 



100 



110 



120 



6k 



standard Density Data Atmospheric Gases and Hydrogen, Pamphlet P-6, 
first ed. (1965), Compressed Gas Association, Inc., New York, N. Y. 

Stewart, R. B. (June, I966) , The Thermodynamic Properties of Oxygen, 
Ph. D. Thesis, Univ. of Iowa, Iowa City. 

Strobridge, T. R. (Jan. I962) , The Thermodynamic Properties of Nitrogen 
from 6k to 200 Atmospheres, Natl. Bur. Stds. Tech. Note No. 129; and 
Strobridge, T. R. (Feb. I963) , The Thermodynamic Properties of Nitrogen 
from 114 to ^kO°B. between 1.0 and 3OOO PSIA, Supplement A (British Units), 
Natl. Bur. Stds. Tech. Note No. 129 A. 

Weber, L. A., D. E. Diller, H. M. Roder, and R. D. Goodwin (I962) , "The 
Vapour Pressure of 20**K Eq.uilibrium Hydrogen," Cryogenics 2, 236-8. 

Weber, L. A. (1968) to be published. 

Woolley, Harold W. , Russell B. Scott, and F. G. Brickwedde (Nov. 1948), 
Compilation of Thermal Properties of Hydrogen in Its Various Isotopic 
and Ortho-Para Modifications , J. Res . , NBS 4l , 379-^75 . 

10 . Appendix 

Units and Conversions 

The calculations for all fluids were performed with equations 

whose units were atmospheres, degrees Kelvin, and molar volumes. The 

various units presented in the tables involved the following conversion 

factors (lUPAC I96I and Mechtly 1964): 

Molecular Weight 

Parahydrogen 2.01594 Ik. 696 PSIA = 1 atmosphere 

Oxygen 31*9988 1.8 degrees R =1 degree K 

Nitrogen 28.OI6 1000.0 cm^ = 1 liter 

Argon 39-948 28.316847 liters = 1 ft^ 

3.7854118 liters = 1 gal 

453.59237 gm = 1 lb 



I 



Acknowledgement 

This work although financed primarily with NBS funds is a "spin- 
off" from the Cryogenics Data Center's data compilation program largely 
supported by NASA-SNPO (Contract R-45) and OART (Contract R-46). 



66 



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